As a 3-D surface display method for representing solid figures on a 2-D display, a display method (e.g., a parametric curved surface method) using functional data and a display method using polygons are available.
To represent, e.g., a sphere using the functional data of the former method is to represent a spherical surface using a parametric curved surface, as shown in FIG. 4A.
According to a representation using polygons of the latter method, a curved surface is represented by a large number of polygons, as shown in FIG. 4B. This method is the most direct and easy method. The display method using polygons is most popular at present.
The state shown in FIG. 4B is the state of data. In the polygonal representation, rendering performed using data represented by a wire frame constituted by straight lines to obtain a solid representation having a sense of reality.
More specifically, in the polygonal representation, polygon data imparted with a connection relationship between straight edges and space coordinates of vertices of a solid figure are displayed.
The following problem is posed in the above polygon representation.
To display a polygon mapped on the pixels of an image, calculations for mapping the contours of a solid figure to be displayed onto pixels and smoothing are required as preprocessing operations.
Therefore, a solid display cannot be performed at high speed. The connection information in the polygon display generally indicates only an order for connecting the vertices of a polygon and does not guarantee a flat surface.
A polygon corresponding to an isoplethic surface and having a large grating point pitch and a large spatial change in sampling value has a polygonal surface not as a flat surface but as a twisted surface if the polygon is a figure having four or more vertices. For this reason, data processing is erroneously performed depending on a hidden line processing in a 3-D surface display, often resulting in an erroneous image.